Those lecture notes comprise a guided travel to the Novikov Conjecture and similar conjectures as a result of Baum-Connes, Borel and Farrell-Jones. they start with fundamentals approximately greater signatures, Whitehead torsion and the s-Cobordism Theorem. Then an creation to surgical procedure concept and a model of the meeting map is gifted.

This quantity comprises 3 lengthy lecture sequence by way of J. L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their subject matters are respectively the relationship among algebraic K-theory and the torsion algebraic cycles on an algebraic type, a brand new method of Iwasawa thought for Hasse-Weil L-function, and the functions of arithemetic geometry to Diophantine approximation.

Knot conception is one zone of arithmetic that has a major variety of purposes. the particular performance of many organic molecules is derived principally incidentally they twist and fold when they are created. through the years, loads of arithmetic has been invented to explain and examine knots.